//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP___RANDOM_POISSON_DISTRIBUTION_H
#define _LIBCPP___RANDOM_POISSON_DISTRIBUTION_H

#include <__config>
#include <__random/clamp_to_integral.h>
#include <__random/exponential_distribution.h>
#include <__random/is_valid.h>
#include <__random/normal_distribution.h>
#include <__random/uniform_real_distribution.h>
#include <cmath>
#include <iosfwd>
#include <limits>

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#  pragma GCC system_header
#endif

_LIBCPP_PUSH_MACROS
#include <__undef_macros>

_LIBCPP_BEGIN_NAMESPACE_STD

template<class _IntType = int>
class _LIBCPP_TEMPLATE_VIS poisson_distribution
{
    static_assert(__libcpp_random_is_valid_inttype<_IntType>::value, "IntType must be an integer type larger than char");
public:
    // types
    typedef _IntType result_type;

    class _LIBCPP_TEMPLATE_VIS param_type
    {
        double __mean_;
        double __s_;
        double __d_;
        double __l_;
        double __omega_;
        double __c0_;
        double __c1_;
        double __c2_;
        double __c3_;
        double __c_;

    public:
        typedef poisson_distribution distribution_type;

        explicit param_type(double __mean = 1.0);

        _LIBCPP_INLINE_VISIBILITY
        double mean() const {return __mean_;}

        friend _LIBCPP_INLINE_VISIBILITY
            bool operator==(const param_type& __x, const param_type& __y)
            {return __x.__mean_ == __y.__mean_;}
        friend _LIBCPP_INLINE_VISIBILITY
            bool operator!=(const param_type& __x, const param_type& __y)
            {return !(__x == __y);}

        friend class poisson_distribution;
    };

private:
    param_type __p_;

public:
    // constructors and reset functions
#ifndef _LIBCPP_CXX03_LANG
    _LIBCPP_INLINE_VISIBILITY
    poisson_distribution() : poisson_distribution(1.0) {}
    _LIBCPP_INLINE_VISIBILITY
    explicit poisson_distribution(double __mean)
        : __p_(__mean) {}
#else
    _LIBCPP_INLINE_VISIBILITY
    explicit poisson_distribution(double __mean = 1.0)
        : __p_(__mean) {}
#endif
    _LIBCPP_INLINE_VISIBILITY
    explicit poisson_distribution(const param_type& __p) : __p_(__p) {}
    _LIBCPP_INLINE_VISIBILITY
    void reset() {}

    // generating functions
    template<class _URNG>
        _LIBCPP_INLINE_VISIBILITY
        result_type operator()(_URNG& __g)
        {return (*this)(__g, __p_);}
    template<class _URNG> result_type operator()(_URNG& __g, const param_type& __p);

    // property functions
    _LIBCPP_INLINE_VISIBILITY
    double mean() const {return __p_.mean();}

    _LIBCPP_INLINE_VISIBILITY
    param_type param() const {return __p_;}
    _LIBCPP_INLINE_VISIBILITY
    void param(const param_type& __p) {__p_ = __p;}

    _LIBCPP_INLINE_VISIBILITY
    result_type min() const {return 0;}
    _LIBCPP_INLINE_VISIBILITY
    result_type max() const {return numeric_limits<result_type>::max();}

    friend _LIBCPP_INLINE_VISIBILITY
        bool operator==(const poisson_distribution& __x,
                        const poisson_distribution& __y)
        {return __x.__p_ == __y.__p_;}
    friend _LIBCPP_INLINE_VISIBILITY
        bool operator!=(const poisson_distribution& __x,
                        const poisson_distribution& __y)
        {return !(__x == __y);}
};

template<class _IntType>
poisson_distribution<_IntType>::param_type::param_type(double __mean)
    // According to the standard `inf` is a valid input, but it causes the
    // distribution to hang, so we replace it with the maximum representable
    // mean.
    : __mean_(isinf(__mean) ? numeric_limits<double>::max() : __mean)
{
    if (__mean_ < 10)
    {
        __s_ = 0;
        __d_ = 0;
        __l_ = _VSTD::exp(-__mean_);
        __omega_ = 0;
        __c3_ = 0;
        __c2_ = 0;
        __c1_ = 0;
        __c0_ = 0;
        __c_ = 0;
    }
    else
    {
        __s_ = _VSTD::sqrt(__mean_);
        __d_ = 6 * __mean_ * __mean_;
        __l_ = _VSTD::trunc(__mean_ - 1.1484);
        __omega_ = .3989423 / __s_;
        double __b1_ = .4166667E-1 / __mean_;
        double __b2_ = .3 * __b1_ * __b1_;
        __c3_ = .1428571 * __b1_ * __b2_;
        __c2_ = __b2_ - 15. * __c3_;
        __c1_ = __b1_ - 6. * __b2_ + 45. * __c3_;
        __c0_ = 1. - __b1_ + 3. * __b2_ - 15. * __c3_;
        __c_ = .1069 / __mean_;
    }
}

template <class _IntType>
template<class _URNG>
_IntType
poisson_distribution<_IntType>::operator()(_URNG& __urng, const param_type& __pr)
{
    static_assert(__libcpp_random_is_valid_urng<_URNG>::value, "");
    double __tx;
    uniform_real_distribution<double> __urd;
    if (__pr.__mean_ < 10)
    {
         __tx = 0;
        for (double __p = __urd(__urng); __p > __pr.__l_; ++__tx)
            __p *= __urd(__urng);
    }
    else
    {
        double __difmuk;
        double __g = __pr.__mean_ + __pr.__s_ * normal_distribution<double>()(__urng);
        double __u;
        if (__g > 0)
        {
            __tx = _VSTD::trunc(__g);
            if (__tx >= __pr.__l_)
                return _VSTD::__clamp_to_integral<result_type>(__tx);
            __difmuk = __pr.__mean_ - __tx;
            __u = __urd(__urng);
            if (__pr.__d_ * __u >= __difmuk * __difmuk * __difmuk)
                return _VSTD::__clamp_to_integral<result_type>(__tx);
        }
        exponential_distribution<double> __edist;
        for (bool __using_exp_dist = false; true; __using_exp_dist = true)
        {
            double __e;
            if (__using_exp_dist || __g <= 0)
            {
                double __t;
                do
                {
                    __e = __edist(__urng);
                    __u = __urd(__urng);
                    __u += __u - 1;
                    __t = 1.8 + (__u < 0 ? -__e : __e);
                } while (__t <= -.6744);
                __tx = _VSTD::trunc(__pr.__mean_ + __pr.__s_ * __t);
                __difmuk = __pr.__mean_ - __tx;
                __using_exp_dist = true;
            }
            double __px;
            double __py;
            if (__tx < 10 && __tx >= 0)
            {
                const double __fac[] = {1, 1, 2, 6, 24, 120, 720, 5040,
                                             40320, 362880};
                __px = -__pr.__mean_;
                __py = _VSTD::pow(__pr.__mean_, (double)__tx) / __fac[static_cast<int>(__tx)];
            }
            else
            {
                double __del = .8333333E-1 / __tx;
                __del -= 4.8 * __del * __del * __del;
                double __v = __difmuk / __tx;
                if (_VSTD::abs(__v) > 0.25)
                    __px = __tx * _VSTD::log(1 + __v) - __difmuk - __del;
                else
                    __px = __tx * __v * __v * (((((((.1250060 * __v + -.1384794) *
                           __v + .1421878) * __v + -.1661269) * __v + .2000118) *
                           __v + -.2500068) * __v + .3333333) * __v + -.5) - __del;
                __py = .3989423 / _VSTD::sqrt(__tx);
            }
            double __r = (0.5 - __difmuk) / __pr.__s_;
            double __r2 = __r * __r;
            double __fx = -0.5 * __r2;
            double __fy = __pr.__omega_ * (((__pr.__c3_ * __r2 + __pr.__c2_) *
                                        __r2 + __pr.__c1_) * __r2 + __pr.__c0_);
            if (__using_exp_dist)
            {
                if (__pr.__c_ * _VSTD::abs(__u) <= __py * _VSTD::exp(__px + __e) -
                                                   __fy * _VSTD::exp(__fx + __e))
                    break;
            }
            else
            {
                if (__fy - __u * __fy <= __py * _VSTD::exp(__px - __fx))
                    break;
            }
        }
    }
    return _VSTD::__clamp_to_integral<result_type>(__tx);
}

template <class _CharT, class _Traits, class _IntType>
basic_ostream<_CharT, _Traits>&
operator<<(basic_ostream<_CharT, _Traits>& __os,
           const poisson_distribution<_IntType>& __x)
{
    __save_flags<_CharT, _Traits> __lx(__os);
    typedef basic_ostream<_CharT, _Traits> _OStream;
    __os.flags(_OStream::dec | _OStream::left | _OStream::fixed |
               _OStream::scientific);
    return __os << __x.mean();
}

template <class _CharT, class _Traits, class _IntType>
basic_istream<_CharT, _Traits>&
operator>>(basic_istream<_CharT, _Traits>& __is,
           poisson_distribution<_IntType>& __x)
{
    typedef poisson_distribution<_IntType> _Eng;
    typedef typename _Eng::param_type param_type;
    __save_flags<_CharT, _Traits> __lx(__is);
    typedef basic_istream<_CharT, _Traits> _Istream;
    __is.flags(_Istream::dec | _Istream::skipws);
    double __mean;
    __is >> __mean;
    if (!__is.fail())
        __x.param(param_type(__mean));
    return __is;
}

_LIBCPP_END_NAMESPACE_STD

_LIBCPP_POP_MACROS

#endif // _LIBCPP___RANDOM_POISSON_DISTRIBUTION_H
